Is it okay to combine Log-in and Sign-up for passwordless/magic-link logins?

The generally received wisdom online seems to be to keep your log-in and sign-up/register flows separate. The reason being, that they are very similar and it is easy for users to get confused.

I plan on using a passwordless system, where users enter an email address and are sent a link to complete their login. The only information I collect about my users though is their email addresses. As such the process for logging in and registering are not just similar, they are exactly the same.

Login:

  • You enter your email address
  • You get sent a link
  • You click the link to log in

Registration

  • You enter your email address
  • You get sent a link
  • You click the link to log in

I was thinking of having a login/register form consisting of an email address field, and a button that simply says "Log in / Register". In either case, you are told an email has been sent to the address entered to login.

My Question

  • Are there any major UX problems with this approach?
  • Do the reasons for separating log-in and sign-up still apply?